Scattering of sound from a point source by a rough surface progressing over an isovelocity ocean

Harper, E. Y.; Labianca, F. M.

doi:10.1121/1.380679

Cited by 13 publications

(7 citation statements)

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“…(2.5) in the case where g(x) ϵ 0, that is, for a flat surface. In this case, the law of reflection gives, for y Ͼ 0, 6) and, more generally, if replaced by ␦g(x), are sought in the form of a perturbation series:…”

Section: B Field Expansionsmentioning

confidence: 99%

“…Indeed, it was these characteristics that prompted a number of investigations in the last 30 years, mainly in the area of scattering by rough surfaces, and that resulted in a variety of low-order theories (see, e.g., Refs. [2][3][4][5][6][7][8][9]. The efficiency of these approaches naturally led to consideration of their applicability and accuracy; despite significant advances in the elucidation of these properties over the last decade, some important aspects remain unresolved.…”

Section: Introductionmentioning

confidence: 99%

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Shape deformations in rough-surface scattering: cancellations, conditioning, and convergence

2004

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We analyze the conditioning properties of classical shape-perturbation methods for the prediction of scattering returns from rough surfaces. A central observation relates to the identification of significant cancellations that are present in the recurrence relations satisfied by successive terms in a perturbation series. We show that these cancellations are precisely responsible for the observed performance of shape-deformation methods, which typically deteriorates with decreasing regularity of the scattering surfaces. We further demonstrate that the cancellations preclude a straightforward recursive estimation of the size of the terms in the perturbation series, which, in turn, has historically prevented the derivation of a direct proof of its convergence. On the other hand, we also show that such a direct proof can be attained if a simple change of independent variables is effected in advance of the derivation of the perturbation series. Finally, we show that the relevance of these observations goes beyond the theoretical, as we explain how they provide definite guiding principles for the design of new, stabilized implementations of methods based on shape deformations.

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Section: B Field Expansionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shape deformations in rough-surface scattering: cancellations, conditioning, and convergence

2004

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“…Besides the simplicity of their implementations, perturbation approaches generally lead, quite efficiently, to very accurate results within their domain of applicability. Indeed, it was these characteristics that prompted a number of investigations in the last thirty years, mainly in the area of scattering by rough surfaces, and which resulted in a variety of low-order theories [21,[29][30][31][32][33][34][35]. The low-order nature of these approaches, of course, restricts their use to the analysis of rather small perturbations of a basic scattering surface, and thus it can severely limit their applicability.…”

Section: The Methods Of Variation Of Boundaries [23 24 27]mentioning

confidence: 97%

High-order numerical solutions in frequency-independent computational times for scattering applications associated with surfaces with composite roughness

Reitich

Turc

2008

Waves in Random and Complex Media

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We introduce a new numerical scheme capable of producing, in frequency independent computational times, high-order solutions to scattering problems associated with surfaces with composite roughness. The procedure can be interpreted as providing a high-order version of the classical (low-order) two-scale method and, as such, it can produce solutions of significantly higher quality with comparable computational effort. The basic strategy consists of a suitable combination of (1) a high-order boundary perturbation treatment that views the highly oscillatory components of the surface as a (possibly large) deformation of the slowly varying portion; and (2) an accurate solution method applicable to single-scattering configurations for the sequence of high-frequency scattering problems that results from (1), which entails a fixed, frequency-independent computational cost. More precisely, the boundary variation procedure in (1) allows for the representation of the fields as a convergent sum of terms which are recursively defined as solutions to scattering problems on the slowly varying portion of the surface, with high-frequency incidences that are derived from its highly oscillatory components.

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“…This avoids the necessity of making some sort of an explicit frozen surface approximation. Several of the most familiar treatments [3][4][5] of the SWHA perturbation theory for scattering from moving surfaces avoid the frozen surface approximation in this manner.…”

Section: Introductionmentioning

confidence: 99%

The role of the frozen surface approximation in small wave-height perturbation theory for moving surfaces

Keiffer

Novarini

Scharstein

2003

The Journal of the Acoustical Society of America

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In the standard development of the small wave-height approximation (SWHA) perturbation theory for scattering from moving rough surfaces [e.g., E. Y. Harper and F. M . Labianca, J. Acoust. Soc. Am. 58, 349-364 (1975) and F. M. Labianca and E. Y. Harper, J. Acoust. Soc. Am. 62, 1144-1157 (1977)] the necessity for any sort of frozen surface approximation is avoided by the replacement of the rough boundary by a flat (and static) boundary. In this paper, this seemingly fortuitous byproduct of the small wave-height approximation is examined and found to fail to fully agree with an analysis based on the kinematics of the problem. Specifically, the first order correction term from the standard perturbation approach predicts a scattered amplitude that depends of the source wave number, whereas the kinematics point to a scattered amplitude that depends on the scattered wave number. It is shown that a perturbation approach in which an explicit frozen surface approximation is made before the SWHA is invoked predicts (first order) scattered amplitudes that are in agreement with the analysis based on the kinematics.

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Scattering of sound from a point source by a rough surface progressing over an isovelocity ocean

Cited by 13 publications

References 0 publications

Shape deformations in rough-surface scattering: cancellations, conditioning, and convergence

Shape deformations in rough-surface scattering: cancellations, conditioning, and convergence

High-order numerical solutions in frequency-independent computational times for scattering applications associated with surfaces with composite roughness

The role of the frozen surface approximation in small wave-height perturbation theory for moving surfaces

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